Session N59: Noninteracting Topological Insulators and Topological Crystalline Insulators in Solid-State Materials

High Spin-Chern-Number Insulator in α-Antimonene

We report on a new topological phase characterized by a high-number quantized Spin Hall conductivity in α-Sb, which we have found in investigating the electronic structures of monolayer α-phase group V elements. This distinct topological phase is invisible in the symmetry-based topological quantum chemistry (TQC) and symmetry indicators (SIs). Since α-As and Sb share the same band representations at high-symmetry points, they are both trivial insulators in terms of TQC and SIs. However, we demonstrate that there is a topological phase transition between As and Sb that involves a band-gap closing at two k-points on the high-symmetry line X-Γ-X. In the absence of spin-orbit coupling (SOC), As is a trivial insulator, while Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of S_z-conserved SOC gaps out the DPs and induces a nontrivial Berry curvature and drives Sb into the new high-spin Chern number topological phase. The band structure of α-Bi differs from that of Sb by a band inversion at Γ, transforming Bi into a Z₂ topological insulator. Our study shows that quantized spin Hall conduc- tivity can serve as a topological invariant beyond the Z₂ topological invariant for characterizing the topological phases.   

Transport measurements in Porous Bi2Te3 thin films

Recent theoretical work has predicted the existence of disordered topological insulators [1, 2], however, minimal experimental work has been conducted on disordered TIs. Here we used molecular-beam epitaxy (MBE) to grow Bi₂Te₃ thin films that were comprised of nanocrystals embedded in an amorphous matrix. Further disorder was introduced through Ne ion irradiation which produced porosity in the films.

In this talk we will present magnetoresistance measurements on porous Bi₂Te₃, where weak anti-localisation (WAL) was observed. The magnetoresistance curves were fitted using a Dirac Fermion model specifically derived to model weak antilocalization in TIs [3]. Our results also show that the temperature dependence of the phase coherence length in porous Bi₂Te_3, with an increased surface to volume ratio, exhibits 2D-like transport.   

Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe

We investigate the effect of a non-magnetic donor impurity located at the surface of the SnTe topological crystalline insulator. In particular, the changes on the surface states due to a Sb impurity atom are analyzed by means of ab-initio simulations of pristine and impurity-doped SnTe. Both semi-infinite and slab geometries are considered within the first-principles approach. Furthermore, minimal and Green's function continuum models are proposed with the same goal. We find that the Dirac cones are shifted down in energy upon doping; this shift strongly depends on the position of the impurity with respect to the surface. In addition, we observe that the width of the impurity band presents an even-odd behavior by varying the position of the impurity. This behavior is related to the position of the nodes of the wave function with respect to the surface, and hence it is a manifestation of confinement effects. We compare slab and semi-infinite geometries within the ab-initio approach, demonstrating that the surface states remain gapless and their spin textures are unaltered in the doped semi-infinite system. In the slab geometry, a gap opens due to hybridization of the states localized at opposite surfaces. Finally, by means of a continuum model, we extrapolate our results to arbitrary positions of the impurity, clearly showing a non-monotonic behavior of the Dirac cone.   

Resolving the topological classification of bismuth with topological defects

Bismuth, due to its large spin-orbit coupling, plays a fundamental role in many topological materials. Yet the topological classification of pure Bismuth has remained, thus far, rather ambiguous. While some theoretical models indicate its trivial topological nature, other theoretical and experimental studies suggest non-trivial topological classifications, such as a strong or a higher order topological insulator. I will explain the origin for this ambiguity and present scanning tunneling microscopy and spectroscopy data in which we resolve the topological classification of Bismuth, as a strong topological insulator with weak indices, by spectroscopically mapping the response of its boundary modes to a topological defect in the form of a screw dislocation [1].  

[1] Nayak et. al., Sci. Adv., 5, eaax6996 (2019)   

Derivation of effective Hamiltonian for Na2XY (X=Mg,Cd;Y=Pb,Sn) dual topological insulators via k.p theory

Dual topological insulators (DTIs) are characterized by spin and mirror Chern numbers – stemming from time reversal and crystalline symmetries, respectively – that make them more robust as compared to ordinary TIs. Here, we apply the k.p method [1] and theory of invariants [2] to derive an effective Hamiltonian for Na₂XY (X=Mg,Cd;Y=Pb,Sn) materials, predicted to be quasi-2D DTIs by ab-initio calculations. The next step is to calculate the topological invariants and investigate the behavior of the edge states and their robustness in the presence of an external magnetic field. Our study is important for a better understanding of DTIs, specially Na₂XY, and their potential applications. The authors acknowledge Julian Zanon for helpful discussions.

[1] R. S. Calsaverini, E. Bernardes, J. C. Egues and D. Loss. Phys. Rev. B 78, 155313 (2008).

[2] J. Fu, P. H. Penteado, D. R. Candido, G. J. Ferreira, D. P. Pires, E. Bernardes and J. C. Egues. Phys. Rev. B 101, 134416 (2020).   

Magnetic field induced charge symmetry in the bulk of the topological insulators Bi2Se3 and Bi2Te3 investigated with NMR

Experiments on 3-dimensional topological insulators focus on the characterization of the special, gapless surface states that emerge as a consequence of the bulk energy band inversion. The bulk states, however, are important, as well, as they provide a direct access to the topologically non-trivial band structure. For example, with nuclear magnetic resonance (NMR) we were able to measure the real-space fingerprint of the bulk energy band inversion, i.e. the redistribution of charges in the chemical structure, in the model topological insulator Bi₂Se₃ [1]. In this system, free carriers as induced by self-doping play a key role because they populate those bands subject to the band inversion. Our measurements further reveal that these conducting electrons possess special properties governed by a strong spin-orbit interaction [1-3]. We show on the basis of a comprehensive experimental evidence from ²⁰⁹Bi NMR in Bi₂Se₃ and Bi₂Te₃ how the local charge symmetry at the nuclear site apparently follows the external magnetic field. This behavior may constitute a so far undocumented rotational degree of freedom of strongly spin-orbit coupled conduction electrons with partially unquenched orbital angular momentum.   

Evidence for 2D conduction channels in hydrogenated Bi2Te3

Topological insulators are quantum solids with metallic surface states that have Dirac band structure and are immune to backscattering by the nonmagnetic disorder. However, ubiquitous charged bulk defects pull the Fermi energy into the bulk, denying access to surface charge transport. We demonstrate that by inserting/removing ionic hydrogen H⁺ in a bulk Bi₂Te₃ crystal, with hole densities in the 10²⁰ cm^-3 range, these defects can be compensated, moving the Fermi level across the charge neutral point (CNP) into the bulk gap. The magnetoresistance R_xx(H) evolves from a quadratic field dependence of a typical bulk metal into a weak antilocalization (WAL) regime with a characteristic low-field cusp near the CNP. From the fits to weak localization theory we obtain the cusp parameter α≅1.004 ± 0.005, corresponding to two 2D quantum conduction channels supported by top and bottom surfaces. The obtained temperature dependence of the dephasing length l_φ ∝1/√T is characteristic of the 2D quantum interference. The 2D character is further confirmed by the scaling of R_xx(H) with the out-of-plane field component H⊥= Hcos??. Our results show that the 2D quantum transport can be accessed by hydrogenation disregarding the 3D bulk size.    

Tunable emergent topological surface states in Sb/Bi2Te3 and Bi2Te3/Sb thin-film heterostructures

Tuning the Dirac surface states of topological insulators (TIs) to achieve desirable surface properties is crucial for developing advanced TI-based electronics, but readily tunable TIs are limited. Our study of synthesized Sb/Bi₂Te₃ and the reversed Bi₂Te₃/Sb topological thin-film heterostructures, reported herein, illustrates a way to substantially broaden the class of tunable systems. In bulk form, Sb (a semimetal) and Bi₂Te₃ (an insulator) both host topological surface states with the invariant Z₂ = –1, whereas ultrathin Sb and Bi₂Te₃ films by themselves are fully gapped insulators. Photoemission band mappings, together with theoretical simulations of the band structure, reveal that in the single-layer Sb limit, the Sb/Bi₂Te₃ heterostructure supports emergent topological surface states strongly localized at the Sb surface. Further Sb coverage leads to a thickness-mediated evolution of the topological surface states along with a shift in the Dirac point energy. This heterostructure thus function as a TI with tunable surface properties controlled by Sb film thickness. These results and related data from the complementary system Bi₂Te₃/Sb will be presented.    

Withdrawn

Prototypical weak topological insulators (WTI) have been theoretically predicted to be realized in quasi-one-dimensional materials Bi4X4 (X = Br, I) [PRL 116, 066801 (2016)] and then experimentally confirmed via ARPES [PRX 11, 031042 (2021) & Nature 566, 518 (2019)]. The unique surface states of such a WTI have two entangled Dirac cones with strong anisotropy. We study theoretically the integer quantum Hall effect of such WTI surface states and show the important roles played by the special geometry, symmetry, topology, and their interplay in Bi4X4. We also predict prominent signatures in transport experiments.   

Persistent negative THz photoconductivity in the vertical topological p-n junction Sb2Te3/Bi2Te3

A thin-film heterostructure of Sb₂Te₃ and Bi₂Te₃ can function as a vertical topological p-n junction with a layer-dependent Fermi level. The spatial separation of the intrinsically p and n doped topological surface states makes this structure a promising candidate for realizing a topological exciton condensate. Here we perform infrared pump-THz probe measurements on epitaxial Sb₂Te₃/Bi₂Te₃ heterostructures to track the real and imaginary parts of the optical conductivity in response to photoexcitation. After the initial free carrier excitation and decay on the order of a few ps, a persistent negative photoconductivity (NPC) is observed over a time > 1 ns. The NPC shows a strong temperature dependence and is only present below 100 K. We will discuss various sources of the NPC in terms of possible exciton formation, lattice heating or scattering between the topological surface states and localized defect states.   

Resonant tunneling between Landau levels formed in topological insulator surfaces realized in epitaxially grown van der Waals heterostructures

Tunneling spectroscopy in van der Waals heterostructures with highly crystalline and atomically sharp interfaces provides a powerful tool to probe the density of states of the materials and the selection rule of tunneling electrons. Here, we present the fabrication and electric transport characterization of vertical tunnel junctions made of topological insulators (TIs) separated by an a-few-atom-thick hBN tunnel barrier. We grow Bi₂Se₃ and Sb₂Te₃, which are n– and p–type TIs, respectively, on both sides of suspended ultrathin hBN layers using molecular beam epitaxy. Our high-resolution transmission electron microscopy reveals an atomically abrupt and epitaxial interface between the hBN substrate and the top- and bottom-TIs. We perform field-angle-dependent magneto-tunneling spectroscopy on the junctions and observe energy-momentum-spin resonance of Dirac electrons tunneling between helical Landau levels developed in the topological surface states.   

Quantum transport in patterned SnTe

SnTe belongs to the class of topological crystalline insulators (TCI), which have non-trivial conducting states where the mirror symmetry is broken at surfaces and edges. To study this behavior, we synthesize SnTe films using molecular beam epitaxy (MBE). The films have high surface area and edge length to volume ratios, which is achieved by growing films patterned with a semi-regular array of square vacancies (200 nm x 200 nm). To measure the effect of these vacancies on electronic conduction, we compare quantum transport measurements on both patterned and unpatterned films. The magnetoconductivity results are fitted with the Hikami-Larkin-Nagaoka (HLN) equation and reveal a mixture of weak localization and weak antilocalization (WL/WAL), which indicates conduction in spin-momentum locked electronic states. The stronger WAL effect at higher temperatures (5K to 10K) in the patterned films shows the suppression of bulk conduction by the presence of square vacancies, and the limited coherence length at low temperatures (2K to 5K) is consistent with scattering at the vacancy boundaries.   

Bi4Br4-based high-temperature quantum spin Hall physics

The manifestation of quantum phenomena at room temperatures is a major challenge but also a major goal in physics, and this is particularly true for the quantum spin Hall effect. Here we report the theoretical demonstration of a variety of high-temperature (and in some cases even room-temperature) quantum spin Hall systems based on Bi₄Br₄, a rare higher-order topological insulator identified recently. We also common on the key experimental studies.   

Nanofabrication and transport studies of Quasi-one-dimensional Topological Insulators

Quasi-one-dimensional (1D) topological insulators (TIs) promise advantages over their three-dimensional (3D) and quasi-two-dimensional (2D) counterparts, such as multiple cleavage planes, strain-induced phase transitions between weak TI, strong TI, and trivial insulator, and hosting of prototype higher-order TIs with helical hinge modes. Prototypical examples of quasi-1D TIs are Bi4I4 and Bi4Br4, which are composed of a periodic stack of atomic chains aligned to the b direction. Utilizing nanofabrication techniques, we are able to exfoliate and fabricate thin layer of field-effect transistors based on these materials and observe their transport behavior at high magnetic field and low temperature.